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What is the median of the following data? 17, 54, 51, 64, 13, 39, 23, 40, 78, 66, 96
52
51.5
50.5
51
51
Arrange the numbers by looking at their tens digit first (10s, 30s, 40s, 50s, 60s, 70s, 90s) to quickly order them without rewriting the whole set, then identify the middle value.
The data set provided is: 17, 54, 51, 64, 13, 39, 23, 40, 78, 66, 96.
Median=(2n+1тАЛ)th┬аterm┬аfor┬аodd┬аn
Arrange the numbers by looking at their tens digit first (10s, 30s, 40s, 50s, 60s, 70s, 90s) to quickly order them without rewriting the whole set, then identify the middle value.
The most common error is failing to sort the data in ascending order before picking the middle value; students often pick the middle value of the unsorted sequence.
Sort the data in ascending order
To find the median, the data must be arranged from smallest to largest.
13,17,23,39,40,51,54,64,66,78,96
Count the total number of observations
Count the elements in the sorted list. There are n=11 elements.
n=11
Apply the median formula
Since n is odd, the median is the value at the 2n+1тАЛ position.
211+1тАЛ=6th┬аposition
Identify the 6th term
Looking at the sorted sequence: 1st=13, 2nd=17, 3rd=23, 4th=39, 5th=40, 6th=51.
Median=51
D is correct because 51 is the middle value of the sorted data set of 11 numbers.
Median is often paired with Mean and Mode in competitive exams; remember that for a symmetric distribution, Mean = Median = Mode.
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